Module: Edits::Levenshtein

Extended by:
Compare
Defined in:
lib/edits/levenshtein.rb

Overview

Implements Levenshtein distance algorithm.

Determines distance between two string by counting edits, identifying:

  • Insertion
  • Deletion
  • Substitution

Class Method Summary collapse

Methods included from Compare

most_similar

Class Method Details

.distance(seq1, seq2) ⇒ Integer

Note:

A true distance metric, satisfies triangle inequality.

Calculate the Levenshtein (edit) distance of two sequences.

Examples:

Levenshtein.distance('sand', 'hands')
# => 2

Parameters:

  • seq1 (String, Array)
  • seq2 (String, Array)

Returns:

  • (Integer)

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# File 'lib/edits/levenshtein.rb', line 22

def self.distance(seq1, seq2)
  seq1, seq2 = seq2, seq1 if seq1.length > seq2.length

  # array of codepoints outperforms String
  seq1 = seq1.codepoints if seq1.is_a? String
  seq2 = seq2.codepoints if seq2.is_a? String

  rows = seq1.length
  cols = seq2.length
  return cols if rows.zero?
  return rows if cols.zero?

  # Initialize first row of cost matrix.
  # The full initial state where cols=3, rows=2 would be:
  #   [[0, 1, 2, 3],
  #    [1, 0, 0, 0],
  #    [2, 0, 0, 0]]
  last_row = 0.upto(cols).to_a

  rows.times do |row|
    prev_col_cost = row + 1
    seq1_item = seq1[row]

    cols.times do |col|
      # | Xs | Xd |
      # | Xi | ?  |
      # step cost is min of operation costs
      # substitution, deletion, insertion
      cost = [
        last_row[col] + (seq1_item == seq2[col] ? 0 : 1),
        last_row[col + 1] + 1,
        prev_col_cost + 1
      ].min

      # overwrite previous row as we progress
      last_row[col] = prev_col_cost
      prev_col_cost = cost
    end
    last_row[cols] = prev_col_cost
  end

  last_row[cols]
end

.distance_with_max(seq1, seq2, max) ⇒ Integer

Calculate the Levenshtein (edit) distance of two sequences, bounded by a maximum value.

Examples:

Edits::Levenshtein.distance("cloud", "crayon")
# => 5
Edits::Levenshtein.distance_with_max("cloud", "crayon", 2)
# => 2

Parameters:

  • seq1 (String, Array)
  • seq2 (String, Array)
  • max (Integer)

    maximum distance

Returns:

  • (Integer)

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# File 'lib/edits/levenshtein.rb', line 78

def self.distance_with_max(seq1, seq2, max)
  seq1, seq2 = seq2, seq1 if seq1.length > seq2.length

  rows = seq1.length
  cols = seq2.length
  return cols > max ? max : cols if rows.zero?
  return rows > max ? max : rows if cols.zero?
  return max if (cols - rows) >= max

  # array of codepoints outperforms String
  seq1 = seq1.codepoints if seq1.is_a? String
  seq2 = seq2.codepoints if seq2.is_a? String

  # 'infinite' edit distance for padding cost matrix.
  # Can be any value > max[rows, cols]
  inf = cols + 1

  # retain previous row of cost matrix
  last_row = 0.upto(cols).to_a

  rows.times do |row|
    # Ukkonen cut-off
    min_col = row > max ? row - max : 0
    max_col = row + max
    max_col = cols - 1 if max_col > cols - 1

    prev_col_cost = min_col.zero? ? row + 1 : inf
    seq1_item = seq1[row]
    diagonal = cols - rows + row

    min_col.upto(max_col) do |col|
      return max if diagonal == col && last_row[col] >= max

      # | Xs | Xd |
      # | Xi | ?  |
      # substitution, deletion, insertion
      cost = [
        last_row[col] + (seq1_item == seq2[col] ? 0 : 1),
        last_row[col + 1] + 1,
        prev_col_cost + 1
      ].min

      # overwrite previous row as we progress
      last_row[col] = prev_col_cost
      prev_col_cost = cost
    end

    last_row[cols] = prev_col_cost
  end

  last_row[cols] > max ? max : last_row[cols]
end